This invention relates methods and system to detect characteristics of a sequence of n-state symbols with n=2 and n>2. More specifically, it relates to detect if a sequence is a pseudo-random maximum length sequence of n-state symbols.
Sequences of symbols have obtained an increased significance in electronic applications such as telecommunications, cryptology and security. A sequence is defined herein as a series of n-state symbols, wherein a symbol is represented by one or more signals, wherein the one or more signals represent one of n states with either n=2 for binary symbols and n>2 for non-binary symbols. The sequences can be generated from reading a storage medium to create the signals that represent the symbols or by generating the symbols from signal processing devices such as Linear Feedback Shift Registers (LFSRs).
In many cases, it is important to use sequences of n-state symbols that have a characteristic of a pseudo-noise (PN) or maximum-length (ML) sequence. In the binary case one generally determines the auto-correlation of the sequence and one derives from the auto-correlation if the sequence is a PN or ML sequence. In n-state cases with n>2 the auto-correlation graph of an n-state sequence of symbols will show side lobes, which may make it difficult to assess to graphically assess if the sequence is an ML sequence.
Accordingly, novel and improved non-graphical methods and systems are required to assess if a sequence or a part of a sequence is Maximum Length.